Design of Cyclic-Coupled Ring Oscillators with Guaranteed Maximal Phase Resolution

Okko Jarvinen, Vishnu Unnikrishnan, Ilia Kempi, Kari Stadius, Marko Kosunen, Jussi Ryynanen

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Cyclic-coupled ring oscillators (CCRO), which consist of M ring oscillators each with N inverting stages, can be used in time-domain data converters to achieve sub-gate-delay resolution and improved phase noise performance compared to a single ring oscillator (RO). However, CCROs can oscillate in several different oscillation modes, where some modes contain overlapping phases. Such in-phase oscillations severely degrade the performance of a time-domain data converter by undermining the sub-gate-delay of the CCRO. This paper presents a design method to avoid the undesired in-phase oscillation modes, and thus achieve guaranteed maximal phase resolution regardless of the oscillation mode, by properly selecting the CCRO dimensions N and M. We show, both theoretically and with transistor-level simulations, that mode-agnostic maximum phase resolution can be ensured by selecting a prime M together with an N which is co-prime with M.

Original languageEnglish
Title of host publicationIEEE International Symposium on Circuits and Systems, ISCAS 2022
Number of pages4
ISBN (Electronic)978-1-6654-8485-5
Publication statusPublished - 2022
MoE publication typeA4 Article in a conference publication
EventIEEE International Symposium on Circuits and Systems - Austin, United States
Duration: 27 May 20221 Jun 2022

Publication series

NameIEEE International Symposium on Circuits and Systems proceedings
ISSN (Print)0271-4302
ISSN (Electronic)2158-1525


ConferenceIEEE International Symposium on Circuits and Systems
Abbreviated titleISCAS
Country/TerritoryUnited States


  • coprime
  • cyclic-coupled ring oscillator (CCRO)
  • phase resolution
  • prime
  • time-to-digital converter (TDC)


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